Abstract
A superconducting microwave resonator is modified with several weak links to make it nonlinear and operated as a phase-insensitive microwave amplifier. Signal gain is demonstrated by intermodulation with a strong pump. The gain is sharply frequency dependent, and we demonstrate phase dependence by examining correlations between the signal and one idler which is a 3rd order intermodulation product of the pump and signal tones. A calibration procedure is described which is based on measurement of both thermal and quantum noise, revealing that the following HEMT amplifier adds noise at 15 times the quantum limit. When operated as a phase-insensitive amplifier the nonlinear resonator added noise at 2.5 times the quantum limit. Significant power is found at intermodulation products beyond 3rd order, which may be responsible for the inability to reach the quantum limit.PACS Codes: 74.78.-w, 42.65.Yj, 85.25.Cp.
Highlights
1 Introduction Minimal dissipation and a designable nonlinearity are the important attributes of superconductors which are enabling the development of quantum electrodynamic circuits. These attributes are manifested in distributed microwave structures with eigenmodes that are suitably modified by tunnel junctions or weak links to make them nonlinear
5 Discussion and conclusions The peaks in Figure (a) and Figure (b) at integer multiples of Δf correspond to odd order intermodulation products
It is difficult to pin-point the source of these higher order intermodulation products: They may be generated in the nonlinear resonator as a result of expansion coefficients gn with odd n > in Eq ( ), or from the g term in higher order perturbation theory
Summary
Minimal dissipation and a designable nonlinearity are the important attributes of superconductors which are enabling the development of quantum electrodynamic circuits. In the nonlinear resonator studied here we realized phase-insensitive amplification by third-order intermodulation of the signal and pump ( wave mixing) where the idler is at frequency fi = fp – fs. This intermodulation product can be generated by a nonlinear oscillator with a g coefficient only, known as the Duffing oscillator or Kerr nonlinearity. These products are typically not looked for in experiments on parametric amplification, but we found significant power at these frequencies, especially when measuring de-amplification of a signal tone We speculate that this higher order intermodulation is responsible for not being able to efficiently squeeze with our amplifier
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